There is the non-interference PID control shown in FIG. 20 (for example, see the Non-Patent Document 1) as an example of the conventional technology for realizing non-interference control with respect to, for example, a controlled object comprising a plurality of inputs and outputs where an interference exists between them, in other words, a controlled object comprising a plurality of operation amounts to be inputted to the object and a plurality of control amounts from the object where there is a mutual interference between the operation amounts and the control amounts.
A controlled object 30 in this example is a controlled object where there is interference between 2ch of two inputs (u1, u2) and two outputs (y1, y2). P11, P21 P12 and P22 are transfer functions. C11 and C22 are main compensators which respectively output operation amounts u1 and u2, based on differences between control amounts y1 and y2 from the controlled object 30 and targeted values r1 and r2. C12 and C2, are cross controllers for realizing non-interference.
In the foregoing conventional example, the interferential relationship of the controlled object 30 is regarded as matrix, and dimensions of the cross controllers C12 and C21 for realizing the non-interference in an adjuster 31 are decided so that any interference can be eliminated.
When the cross controllers C12 and C21 are designed in such a manner that the control amount y1 is not affected by the operation amount u2′ and the control amount y2 is not affected by the operation amount u1′, any possible interference can be avoided. As a possible method for eliminating such an influence, inverse matrix may be used.
However, the interferential relationship of the controlled object 30 that is a predetermined condition of the example is not a simple and low-level matrix. Therefore, a first model in this conventional example cannot realize an ideal non-interference.
This is due to a reason because the interferential relationship of the controlled object 30 is not such a simple one-way relationship from the operation amounts u to the control amounts y.
The transfer of a heat quantity due to the interference results from a temperature difference. The transfer of the heat quantity due to the interference is large when the temperature difference between a plurality of points of the controlled object is large, while the transfer of the heat quantity due to the interference is small when the temperature difference between the plurality of points of the controlled object is small. Because such a relationship is not taken into account, the assumed model to be controlled generates a significant error, which gives a limit to a factor that can be eliminated through the inverse matrix of the non-interference control.
Therefore, the non-interference control in the conventional manner was often not applicable to practical use.
The Applicant of the present invention has already proposed a model structure suitable for the non-interference control, prediction control and the like as recited in the Patent Document 1.
FIG. 21 is a block diagram illustrating an example of a model structure 1′ thus proposed. The example corresponds to the controlled object 30 in the conventional example shown in FIG. 20.
The model structure 1′ is a thermal model of a controlled object of the thermal interference system provided with two inputs (u1, u2) and two outputs (y1, y2) and also a model of a controlled object comprising two channels.
As the inputs (u1, u2), it is possible to assume operation amounts corresponding to outputs of two heaters for respectively heating the controlled object such as the heat treatment board or the thermal treatment furnace. As the outputs (y1, y2), it is possible to assume control amounts which are temperatures detected from two temperature sensors for respectively detecting a temperature of the controlled object.
The model structure 1′ is a model having a feedback structure which calculates a difference between the two outputs (y1, y2) in a subtracter 2 and feeds back the calculated difference to the two inputs (u1, u2) via a feedback element Pf, and feed back it after changing polarities so as to reverse in positive or negative to each other via a subtracter 3 and an adder 4.
A11, A22 are transfer functions from each of the inputs u1 and u2 to each of the outputs y1 and y2. In the present example, the part allocated to the two heaters of the controlled object such as the heat treatment board or the heat treatment furnace, in other words, the controlled object corresponding to each channel ch, can be grasped as the model element. The respective model elements are shown as the transfer functions A11 and A22.
The model structure 1′ is, for example, the thermal model of the thermal interference system, wherein the heat quantity is transferred when there is any temperature difference. This is equivalent to what the Fourier's law represents, that is, the transfer of the heat quantity is in proportion to the temperature difference.
The Fourier's law is described below. For example, according to Page 6 of “Heat Transfer Engineering” by Hideaki Tasaka, published by Morikita Publishing Co., Ltd., an important factor for deciding a heat transfer amount is a spatial temperature gradient. Provided that a distance between two points is Δx, and a temperature difference between the two points is ΔT, a thermal flow velocity q (heat transfer amount per unit area) is q=−λ(dT/dx) with λ as a thermal conductivity provided that ΔT/Δx is regarded dT/dx.
The feedback element Pf shown in FIG. 21 corresponds to the thermal conductivity λ in the Fourier's law.
According to the model structure 1′, the difference between the two outputs y1 and y2 which are the outputs of the before-mentioned respective model elements, that is, the temperature difference, is fed back to the two inputs u1 and u2 which are the inputs of the respective model elements, that is, the operation amounts corresponding to the heat quantity, after changing the polarities so as to reverse in positive or negative to each other via the feedback element Pf corresponding to a degree of the interference or the like. The drawing is a block diagram which shows such a thermal-interference phenomenon that the heat quantity transfers from one of the channels ch to the other channel ch, and one of the channels ch loses the heat quantity (negative), while the other channel ch gains the heat quantity (positive).
The model structure 1′ represents the Fourier's law that the interference of the thermal object to be controlled means that the heat quantity transfers in proportion to the temperature difference in the case where temperature difference is generated between two temperatures.
The feedback element Pf denotes a ratio of how much heat quantity is transferred depending on the temperature difference, and may be a coefficient value or a first order lag element.    Patent Document 1: No. 2004-94939 of the Japanese Patent Applications Laid-Open    Non-Patent document 1: Page 62 of “PID Control” by Nobuhide Suda and others, published by Asakura Publishing Co., Ltd. on Mar. 10, 2000 (edited by the Institute of Systems, Control and Information Engineers)